In this paper, we consider a nonlinear hybrid dynamic （NHD） system to describe fedbatch culture where there is no analytical solutions and no equilibrium points. Our goal is to prove the strong stability with respec...In this paper, we consider a nonlinear hybrid dynamic （NHD） system to describe fedbatch culture where there is no analytical solutions and no equilibrium points. Our goal is to prove the strong stability with respect to initial state for the NHD system. To this end, we construct corresponding linear variational system （LVS） for the solution of the NHD system, also prove the boundedness of fundamental matrix solutions for the LVS. On this basis, the strong stability is proved by such boundedness.展开更多
基金Project supported by the Russian Foundation for Basic Research,Grant 99-01-00847the Russian Humanitarian Scientific Foundation,Grant 00-02-00152a,by the NNSF of China(19971047) and DSF
文摘In this paper,the asymptotic behavior of generalized risk processes without any momentassumptions on the controlling process is described.
基金This work was supported by the National Science Foundation for the Youth of China （Grant Nos. 11501574, 11401073 and 11701063）, the National Natural Science Foundation of China （Grant Nos. 11771008, 61673083 and 61773086）, the National Science Foundation for the Tianyuan of China （Grant No. 11626053）, the Natural Science Foundation of Shandong Province in China （Grant No.： ZR2015FM014, ZR2015AL010 and ZR2017MA005）, the Fundamental Research Funds for the Cen- tral Universities in China （Grant No. DUT16LK07） and the Project funded by China Postdoctoral Science Foundation （Grant No. 2016M601296）.
文摘In this paper, we consider a nonlinear hybrid dynamic （NHD） system to describe fedbatch culture where there is no analytical solutions and no equilibrium points. Our goal is to prove the strong stability with respect to initial state for the NHD system. To this end, we construct corresponding linear variational system （LVS） for the solution of the NHD system, also prove the boundedness of fundamental matrix solutions for the LVS. On this basis, the strong stability is proved by such boundedness.
